Reproduce “Point Cloud Quality for Meshfree Methods” on OpenResearch
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About this paper
Mohsen Abdolahzadeh, Oleg Davydov, Isabel Michel, Pratik Suchde
The authors test which local point-cloud quality measures track numerical error in meshfree generalized finite difference methods. They perturb grids, solve PDEs with known solutions, and compare 25 measures using Spearman rank correlation. Six measures rank consistently among the strongest. Recovery Error scores 1.38 on elliptic tests and 2 on advection; these relative rankings apply only to tested settings.
Key insights
- Metrics derived from the actual local differentiation system—especially recovery error and weighted ℓ1/ℓ2 growth functions—track meshfree accuracy more consistently than purely geometric measures.
- Fill distance and inter-molecular potential force provide useful lower-cost indicators, whereas separation distance, packing density, uniformity ratio, and average local regularity are weaker predictors.
- Inverse aspect ratio, effective for conventional mesh assessment, does not reliably predict meshfree error after triangulating a point cloud; the choice of global aggregation also affects performance.
Summary by alphaXiv.
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